Such results have found many applications in the literature on various topics in geometric measure theory and related areas including Borel rings in real line, distance sets, orthogonal and radial projections, Besicovitch and Furstenberg sets, and spectral gaps. We refer the reader to [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]} and references therein for more details. A number of generalizations with applications in different settings can also be found in [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]}.
